The following is copied from an online blog: I think there is really a lot more to it than this but, it is true that our device can accelerate at well over 1g continuously. It can also carry several small propellant tanks allowing it to work efficiently in a vacuum. It should also work well with relativistically accelerated propellants... Please see below.
According to Wikipedia, "interstellar travel at 1G would take approximately 1 year + the distance in light-years. Proxima Centauri (4.2 light years) for example would take 5.2 years.
But that time is from the viewpoint of stationary observers at the departure point. The trip's duration from the traveler's viewpoint would be less due to the time dilation effect predicted by Einstein's Theory of Relativity. The greater the distance, the greater the speed from the stationary observer's viewpoint. From the stationary observer's viewpoint the traveler's rate of acceleration would slow as they approached the speed of light. The traveler would see no change between their speed and the speed of light. Instead they would experience time at an increasingly slower rate which would effectively cause the distance to the destination to become shorter.
Due to the time dilation effect, 1G acceleration should be sufficient to travel anywhere in our galaxy in less than a lifetime from the viewpoint of the traveler, but not the stationary observer. "
Also, according to what I have read so far, any destination in the solar system, would be a short trip at 1g.
I welcome any corrections on this, since I didn't have time to run the all of the numbers yet.
The above link has recently been repaired, thanks to some viewers for letting me know.